Accession Number : AD0820743

Title :   ON THE NUMERICAL SOLUTION OF THE GRAVIMETRICAL INTEGRAL EQUATION OF BJERHAMMAR.

Descriptive Note : Final technical rept. Apr 66-Apr 67,

Corporate Author : ROYAL INST OF TECH STOCKHOLM (SWEDEN) GEODESY DIV

Personal Author(s) : Reit, B. G.

Report Date : JUN 1967

Pagination or Media Count : 36

Abstract : In this report an analysis is made of the different mathematical problems arising in practical applications of the new gravity reduction theory of Bjerhammar. The body of the report is to a great extent concentrated upon the solution of the basic integral equation of the theory. Different methods of solutions developed by A. Bjerhammar and W. Foerstner are discussed. An improvement of the methods are suggested, which makes it possible to introduce a great number of unknown coefficients in the linearized equations without being forced to increase the order of the approximating polynomials. The transformation of the integral equation from the sphere to the plane is analyzed in detail. Finally, new formulas are derived, making it possible to integrate the so-called x- and y-parameters for an arbitrary location of the actual point of computation. (Author)

Descriptors :   (*GRAVITY, NUMERICAL ANALYSIS), (*GEODESICS, THEORY), INTEGRAL EQUATIONS, NUMERICAL METHODS AND PROCEDURES, APPROXIMATION(MATHEMATICS), POLYNOMIALS, TRANSFORMATIONS(MATHEMATICS), EARTH(PLANET), PARTIAL DIFFERENTIAL EQUATIONS.

Subject Categories : Geodesy
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE